I would like to know how to solve the problem. Please give me the answer and calculation process.

Problem

Suppose P is drawn from the Uniform[0; 1] distribution, and then conditional on P, another random variable X is drawn from a Bernoulli(P) distribution. (a) Use the tower law to compute P(P t; X = 1) where t E [0; 1] is some constant value. (b) Compute the CDF of the conditional distribution of P given X = 1. (c) Now suppose that, after P is drawn, we instead draw twice from the Bernoulli(P) distribution to produce random variables X and Y , rather than drawing only once to produce X as before. (We assume that, conditional on the value of P, the random variables X and Y are drawn independently.) Calculate P(X = Y ).